Question

consider the following sample data, which represent weights walnuts in grams: { 10.6, 10.9, 11.6, 11.7, 12.9, 13.5, 13.5, 14, 14, 14, 14.4, 14.6, 14.9, 15.4, 16.3, 16.6, 17.2, 17.2, 17.8, 18.5 }. first, give the mean of the data set. part 2 of 6 next, give the median of the data set. part 3 of 6 now give the mode of the data set. if there is more than one, write them in order, separated by commas. part 4 of 6 finally, give the midrange of the data set. part 5 of 6 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will be roughly symmetric. the distribution will probably be skewed to the left. the distribution will probably be skewed to the right. part 6 of 6 suppose the last value in the data set is mistakenly recorded as 185. how would this affect the mean? the mean would get larger. the mean would not change. the mean would get smaller. how would this affect the median? the median would not change. the median would get smaller. the median would get larger.

Explanation:

Step1: Calculate the original mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 20$ and $\sum_{i=1}^{20}x_{i}=10.6 + 10.9+11.6+11.7+12.9+13.5+13.5+14+14+14+14.4+14.6+14.9+15.4+16.3+16.6+17.2+17.2+17.8+18.5 = 292.6$. So $\bar{x}=\frac{292.6}{20}=14.63$.

Step2: Analyze the effect on the mean when the last - value changes

The original sum is $S = 292.6$. If the last value changes from $18.5$ to $185$, the new sum $S'=292.6 - 18.5+185=459.1$. The new mean $\bar{x}'=\frac{459.1}{20}=22.955$. Since $22.955>14.63$, the mean would get larger.

Step3: Analyze the effect on the median when the last - value changes

The data set has $n = 20$ values. The median is the average of the 10th and 11th ordered values. When the last value changes from $18.5$ to $185$, the order of the first 19 values does not change, and the median is still the average of the 10th and 11th ordered values. So the median would not change.

Answer:

For the question "How would this affect the mean?": The mean would get larger.
For the question "How would this affect the median?": The median would not change.